The invention relates to a method and device for the spectral analysis of electromagnetic radiation.
Currently there exist two basic physical approaches to the spectral analysis of light utilizing either the phenomenon of angular separation or interference of light.
In the method based on the angular separation, the analyzed light beam interacts with an appropriate optical element and changes the direction of its propagation depending on the wavelength. This way spectral components are spatially separated and can be independently analyzed. The spatial separation is based either on the dispersion of the refractive index in optical prisms or on the properties of the optical grating where the angle of reflection of the incident radiation depends on the wavelength. Commercially available instruments based on these principles are called monochromators which have been widely used in ultraviolet (UV), visible (VIS) and infrared (IR) spectral regions.
Instruments directly utilizing the interference of light are generally based on the Michelson interferometer. The analyzed light is split into the two interfering light beams and so called xe2x80x9cinterferogramxe2x80x9d is measured as a function of the variable optical path in one arm of the interferometer. The spectrum of the analyzed radiation is then extracted from the interferogram by methods of Fourier-transform analysis. The interferometric techniques are preferentially utilized in the IR spectral region because for longer wavelength it is easier to reach the required accuracy of the position of the movable mirror in the interferometer.
The nature of the invention lies in the utilization of a new physical method for the spectral analysis of electromagnetic radiation, especially light, and in the technical design and construction of devices which utilize this new principle.
The new method according to the present invention utilizes the physical phenomenon known as dispersion of optical rotation, wherein the polarization plane of linearly polarized electromagnetic radiation is rotated during propagation through an active environment of a proper optical element (rotator) and the rotation angle depends on the wavelength of the radiation. If the total intensity of polarized polychromatic radiation is I=∫I(xcex)dxcex, then after passage through the rotator and through an analyzing polarizer (analyzer) the xe2x80x9crotogramxe2x80x9d R(p) can be measured as a function of the parameter p, which characterizes physical and geometrical properties of the rotator:                               R          ⁡                      (            p            )                          =                              ∫            λ                    ⁢                                    I              ⁡                              (                λ                )                                      ⁢                                          cos                2                            ⁡                              [                                                      ϕ                    o                                    +                                      ϕ                    ⁡                                          (                                              λ                        ,                        p                                            )                                                                      ]                                      ⁢                          ⅆ              λ                                                          (        1        )            
wherein I(xcex) is the spectrum of input radiation, xcfx86o denotes an angle between a direction of maximum transmittance of the analyzer and a polarization plane of input radiation, and xcfx86(xcex,p) stands for a rotation angle of the polarization plane of radiation with the wavelength xcex after passage through the rotator. The equation (1) is a Fredholm""s integral equation of the first type (Press W. H., Teukolski S. A., Wetterling W. T. and Flannery B. P.: Integral Equations and Inverse Theory in Numerical Recipies in Fortran, Cambridge University Press, 1992, p.779) with the kernel K(xcex,p)=cos2[xcfx86o+xcfx86(xcex,p)]. If R(p) is measured, I(xcex) can be unambiguously calculated from equation (1) using modern advanced methods of numerical analysis, especially the maximum entropy method (MEM) (Skilling J. and Bryan R. K.: Maximum Entropy Image Reconstruction: General Algorithm, Mon. Not. R. astr. Soc., 211 (1984) 111-124). In the special case of a rotator made from an optically active material with a specific optical rotation D(xcex), the parameter p can represent its adjustable thickness in the direction of the light beam propagation, which gives xcfx86(xcex,p)=pxc2x7D(xcex).
The invention determines a spectrum of electromagnetic radiation, particularly of light characterized by a measurement of a rotogram R(p) of the radiation defined by equation (1), wherein a dispersion element made from an optically active medium exhibiting dispersion of optical rotation, placed between two polarizers with arbitrarily oriented polarization planes, preferably parallel or perpendicular, and subsequent mathematical analysis of the rotogram, preferably by the maximum entropy method, is used to determine the spectrum of the electromagnetic radiation.
In the device based on this principle, the linearly polarized beam of radiation first propagates through an optical rotator where the polarization planes of the individual spectral components are rotated depending on their wavelength xcex, then passes through an analyzer and strikes a detector that measures R(p) as a function of the parameter p. Finally the spectrum I(xcex) is calculated from equation (1).
In an apparatus in accordance with the invention there may be utilized one of the many possible configurations of a rotator, which can be manufactured from optically active left-hand and right-hand-rotating forms of quartz crystals (FIG. 1A). The rotator may comprise two left-hand-rotating (xe2x88x92) prisms 1 and 2 and one right-hand-rotating (+) compensation plate 3. The function of the rotator remains the same when the right-hand-rotating prisms and the left-hand-rotating compensation plate are used. The light beam propagates along a direction of parallel aligned optical axes of all three optical elements. A shift of the larger prism 1 by a distance x along its common plane with the smaller prism 2 from the position when the path d of the beam in the right-hand and left-hand-rotating materials is the same, d(+)=d(xe2x88x92), causes a change of effective thickness of the active environment equal to p=d(+)xe2x88x92d(xe2x88x92)=x sin xcex1. The direction of the movement and the angle xcex1 are depicted in FIG. 1A. For a set of different shifts x the rotogram R(p) can be measured. Then the spectrum I(xcex) can be calculated from the measured R(p).
In some special applications the change of the thickness of the rotator can be a disadvantage. The rotator depicted in FIG. 1B, (Hariharan P., Meas. Sci. Technol. 4 (1993) 136-137), does not suffer from this drawback. The rotator consists of four geometrically identical quartz prisms 13, 14, 15, 16, from which two prisms 13, 16 are made from right-hand-rotating quartz and the other two prisms 14, 15 from left-hand-rotating quartz. The optical axes of all four prisms are again oriented parallel with the optical axis of the rotator and the input light propagates through the rotator in the direction of the axis. A shift of the mutually fixed pair of prisms 15, 16 relative to the other pair of mutually fixed prisms 13, 14, in the direction of the x-axis, perpendicular to the direction of the light propagation, causes a change of the parameter p=d(+)xe2x88x92d(xe2x88x92)=2xc3x97tanxcex1. The change of p is the same over the whole cross section of the beam. Any shift produces a uniform rotation of polarization planes of rays of the same wavelength.
The invention is further a method for determining the spectrum of a point-size source of light in a single-channel setup with a passage of polarized electromagnetic radiation through an optical element which exhibits uniform dispersion of optical rotation the whole cross-section of the beam of radiation. After passage through the analyzing polarizer, the intensity of the radiation is sequentially measured by a single-channel detector as a function of the parameter p. In this case p represents the thickness of the optically active medium in the direction of the beam propagation. Multiple measurements of the output intensity for different values of p creates the rotogram R(p) from which the desired spectrum is calculated.
The invention is further a method for determining a spectrum of electromagnetic radiation of a two-dimensional source of radiation. A multi-channel setup is used. Polarized radiation is passed from a two-dimensional light source through the optical element which exhibits the same dispersion of the optical rotation across a complete cross-section of the input beam of radiation. After passage through the analyzing polarizer, the intensity of the radiation is sequentially measured by a two-dimensional multi-channel detector, which preferably may be a diode matrix. The intensity is a function of the parameter p, which preferably is the thickness of the optically active medium in the direction of the beam propagation. Rotograms R(p), are simultaneously measured for each element of the planar source of radiation by a corresponding element (pixel) of the two-dimensional multi-channel detector. After mathematical analysis, a spectral map of the investigated object (spectral imaging) may be constructed.
The invention is further a method for determining spectra of a point-size light source in a multi-channel setup. Polarized radiation, which is spectrally homogeneous in the whole cross-section of the beam, passes through an optical element, which exhibits variation in the dispersion of optical rotation in a particular direction across the input beam of radiation. After passage through an analyzing polarizer, a dependence of the light intensity in the direction on the parameter p is measured. Preferably, p is a difference in the light-path in the left-hand and right-hand-rotating medium of the optical element given by a proper geometrical shape of the dispersion element which preferably may be wedge-shaped. The rotogram R(p) is simultaneously measured for the whole range of the parameter p by a multi-channel detector or by a group of individual detectors from which the desired spectrum is calculated. Each detector represents an individual value of the rotogram R(p).
The rotator, can be constructed as a sequence of several consecutive optical components made from left-hand and right-hand rotating forms of optically active crystals, which preferably may be quartz. The optical axes of the individual components are all aligned parallel to each other and the analyzed light propagates through the rotator in the direction of the the optical axes.